Continuity mistake: When Homer and Bart arrive at The Enriched Learning Center, they go to the classroom and you can see there is a sign outside the room saying "Learning Center: Grade IV." But when we see the two a little later on, the writing has gone.
Continuity mistake: During the intelligence test, the table on Bart's paper changes between shots.
Continuity mistake: When Bart and the three other boys are standing by the wall after Bart sprayed a drawing of Principal Skinner, there are bushes by the end of the wall. But when we see Martin standing by the drawing, there are no bushes.
Continuity mistake: Millhouse's hair color changes from when we first see him to when Bart comes back to the school yard.
Continuity mistake: At the very start the twins are stood facing each other. Camera cuts to behind and now they are side by side. (00:01:20)
Continuity mistake: On the bus at the start there are some lines on Mrs. Krabbapple's microphone. They disappear when she tells Bart to sit down. (00:03:00)
Continuity mistake: When Sherri and Terri raise their hands and say "like us Mrs. Krabbapple" they raise their hands over their heads. Camera cuts and their hands are a lot lower. (00:04:20)
Other mistake: In this episode, Smithers' skin is brown, however in future episodes, his skin is yellow. (00:05:00)
Audio problem: Just after Mr Smithers says "...so that we have the energy to from your favourite video game to yummy cotton candy machines", all the children start clapping but the sound of clapping starts BEFORE they start clapping. (00:05:05)
Revealing mistake: During the first ten minutes when the twins are explaining to Bart what incompetence means, one of the twins' body disappears, showing a floating head and hair. (00:06:30)
Factual error: After Bart's prank call with Moe, you can see Bart and Lisa laughing. However the telephone's wire does not connect to the receiver. (00:09:40)
Continuity mistake: In the park, Marge's necklace changes from white to red. (00:15:40)
Continuity mistake: At the very end of the episode, when Homer is being carried off by the crowd, you can see that the crowd carrying Homer, the people are small, so you'll have to look closely, but right before the credits, Marge's necklace changes from red to white, back to red and then finishes with white all in one shot. (00:21:00)
There's No Disgrace Like Home - S1-E4
Continuity mistake: The amount of marshmallows in the jelly at the start changes between shots. (00:02:00)
There's No Disgrace Like Home - S1-E4
Continuity mistake: When they put Maggie down in the Creche she is in the middle of a carpet. Camera cuts and now she's at the edge. (00:04:25)
There's No Disgrace Like Home - S1-E4
Audio problem: When Marge gets drunk at the picnic, she falls on Homer while saying "Homie, did you try the punch?", her lips don't move. (00:06:20)
There's No Disgrace Like Home - S1-E4
Continuity mistake: When Homer walks in on the family eating dinner, Marge has her feet on the second cushion of the sofa. Camera changes and now they are on the third cushion. (00:08:50)
There's No Disgrace Like Home - S1-E4
Continuity mistake: When the Simpsons are spying on the old man, the boy and the old woman, all three of them disappear and then reappear between shots. Whenever there is a wide shot from outside the house, they are not there but when there is a close shot from outside or inside they are there. (00:11:00)
There's No Disgrace Like Home - S1-E4
Continuity mistake: As Homer is carrying the TV towards the pawn shop in the first shot the left window is clear. There is then a tracking shot of the family walking and when they get in front of the store the window has writing on it saying Pawn Shop. The writing is in black and the next shot when they are talking the writing is now dark brown. (00:14:20)
There's No Disgrace Like Home - S1-E4
Continuity mistake: When undergoing shock therapy, the doc raises his hands to his head. They are not present in the next shot. (00:19:00)